Conventionally, as a representative image compression scheme, there is a JPEG (Joint Photographic Experts Group) scheme standardized by the ISO (International Organization for Standardization). In this JPEG scheme, an image is split into blocks, a DCT (Discrete Cosine Transform) is applied to each of the blocks to acquire DCT coefficients, the DCT coefficients are quantized, and further entropy encoding is performed, thereby realizing image compression with high quality and high compression ratio.
In recent years, active studies have been made on encoding schemes that split an image into a plurality of bands by filters called a filter bank using a combination of a high-pass filter and a low-pass filter, and perform encoding on a band-by-band basis. Among those, wavelet transform encoding is free from a drawback of DCT that block distortion becomes conspicuous at high compression, and is thus regarded as a new promising technique to supersede DCT.
For example, the JPEG 2000, of which international standardization was completed in January 2001, adopts a compression encoding scheme that combines this wavelet transform with high-efficiency entropy encoding based on bit modeling on a bitplane-by-bitplane basis and arithmetic encoding. With this JPEG 2000 scheme, a significant improvement in encoding efficiency is achieved over the JPEG scheme. Patent Document 1 describes a wavelet transform method in which encoding efficiency is further enhanced.    Patent Document 1: Japanese Unexamined Patent Application Publication No. 9-130800